What Day Will You See the Same Star Rise at 10:40pm?

[dekoi]

Question:
Imagine you go out tonight at 9:00pm and see a star rising on the horizon. If you go out tomorrow at the same time, the star will be in a different location. What day would you be able to see the same star rise from the horizon at 10:40pm?

My half-answer:
The difference between a sidereal and a solar day is that the solar day is ~3.9 min longer.

However, I cannot seem to apply this concept to figure out which day the star would rise at 10:40pm.

I have formulated my own equation,

tn = to - 3.9n

Where tn is the final value of time (in this case, 10:40pm), and to is the original value of time (in this case, 9:00pm). n is the number of days (in this case, what we are trying to find).

By substituting values into my equation, I get:
n = (9:00pm - 10:40pm) / 3.9 min

However, I cannot figure out the answer from that. This is a very easy question but I am really stumped. Any help?

 

[Andre]

How many minutes from 9:00pm to 10:00pm and then how many more from 10:00pm to 10:40pm?

 

[dekoi]

9 -> 10 = 60 min
10 -> 10:40 = 40 min

100 min in total

Then what?

Is it :

100 min / 3.9 min = 25.6

 

[Andre]

n=100/3.9?

 

[dekoi]

I cannot believe I am still confused...

25.6

but 25.6 what?

days? How does that work according to units?

 

[dekoi]

or how about instead of 100 min... 1440 min - 100 min = 1340 min

1340 / 3.9 = 343.6 days?